Distribution coefficients Terms Links

Carrier facilitated transport involves a combination of chemical reaction and diffusion. One way to model the process is to calculate the equilibrium between the various species in the membrane phase and to link them by the appropriate rate expressions to the species in adjacent feed and permeate solutions. An expression for the concentration gradient of each species across the membrane is then calculated and can be solved to give the membrane flux in terms of the diffusion coefficients, the distribution coefficients, and the rate constants for all the species involved in the process [41,42], Unfortunately, the resulting expressions are too complex to be widely used. 

There is experimental evidence to support the estimate that t/H = t/Na in this system. In the research of Travers and one of the present authors (2), a study of the complexation of divalent metal ions by poly-methacrylic acid (PMA) showed that deviation from ideality with a of the divalent ions exposed to the same potential as the H+ ion was described exactly by the deviation term deduced from the potentiometric properties of the PMA. Additional evidence for this estimate is available in the ion-exchange literature (3,4,5). At a relatively low cross-linking percentage (2 wt % divinyl benzene) j/h is about equal to t/Na> as evidenced by the ion-exchange distribution of Na+ and H+ between a polystyrene sulfonate-based resin and a simple dilute electrolyte mixture of Na+ and H+ (Na H+, X"). The selectivity coefficient measured over the complete composition range of the resin deviates very little from unity to demonstrate this as an experimental fact (KHNa = 1.02 zt 0.02... 

Note that when (10.31) is expanded in terms of 4> according to (10.34), the result is a power series in but when (10.33) is averaged over , all terms with odd powers of 4> vanish. This results because it requires two for each linkage. Thus (10.33), if expanded, would be a formal power series in powers of /x. The coefficient of /r" contains all the terms for which there are m cross-links randomly distributed with the proper weights for each of the chain segments. Therefore for m cross-links we must Just take the coefficient of /r" . This can easily be selected by applying the contour integration... 

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